Gauge-invariant rearrangement and theory of the Cabibbo angle

Abstract

Spontaneous breakdown of a global symmetry leads to a rearrangement of the degrees of freedom connected with the broken-symmetry transformations This rearrangement is reinvestigated for a gauge-invariant form of theU1 chiral-invariant andSU2 isospin-invariant nonlinear spinor models of the Nambu-Jona-Lasinio type. The asymmetry of the ground state in connection with the remaining invariance under the corresponding local symmetry establishes two different regimes: the “asymptotic regime” governed by “frozen mass fields”, relevant for the particle interpretation, and the “local regime” dominated, by “unshielded current fields” which is probed by the vector gauge fields. In both regimes the Goldstone-field interactions can be essentially absorbed by an appropriate dressing of the original fields inducing characteristic proliferations of these fields. The proliferated sets of “mass fields” and “current fields” are connected by a well-defined unitary transformation which in case of the spontaneously brokenSU2 symmetry plays the role of the Cabibbo rotation. The Cabibbo angle is related to the strength of the vector-isovector coupling of the four-fermion interaction.